We did it on the Millie 3 years ago at end of June. Very hot that year, june 24th 104 degrees in Rome, wife was pegging out! We flew in with easyjet & did our own trans at Venice by taxi. Did Rome on our own by train. Only ship excursion we used was Barcelona ship to airport with a tour of city. We love the Millie class ships. We usually use the light cafe by the covered pool for BF & lunch. Food is always good.

Hi next year will be the first time Summit has been in the Med. I did the Caribbean on her in her inaugural year.
I have done Venice to Barcelona and Barcelona to Venice on Millennium and loved the itinary. Dubrovnik I love especially. I love Venice and would travel there any number of times. Years ago I did the ship excursions but would not do them now as I think they are too restrictive and also expensive.
If you do a bit of homework and especially on these boards or on Cruise Critic you will get lots of ideas and advice so will easily be able to do things to suit you.

Look forward to it.

Sue